diff --git a/onnxscript/function_libs/torch_lib/ops/core.py b/onnxscript/function_libs/torch_lib/ops/core.py
index c3892c6cd3..14366fc825 100644
--- a/onnxscript/function_libs/torch_lib/ops/core.py
+++ b/onnxscript/function_libs/torch_lib/ops/core.py
@@ -7861,25 +7861,18 @@ def aten_square(self: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::squeeze")
+@torch_op("aten::squeeze", trace_only=True)
 def aten_squeeze(self: TTensor) -> TTensor:
     """squeeze(Tensor(a) self) -> Tensor(a)"""
 
     return op.Squeeze(self)
 
 
-@torch_op("aten::squeeze.dim")
+@torch_op("aten::squeeze.dim", trace_only=True)
 def aten_squeeze_dim(self: TTensor, dim: int) -> TTensor:
-    result = self
-    if Rank(self) > 0:  # type: ignore[operator]
-        # check if specified dimension is 1, do squeeze
-        shape = op.Shape(self)
-        dim_size = op.Gather(shape, dim, axis=0)
-        if dim_size == 1:
-            dims = op.Reshape(dim, op.Constant(value_ints=[-1]))
-            result = op.Squeeze(self, dims)
-
-    return result
+    if len(self.shape) == 0:
+        return self
+    return op.Squeeze(self, [dim])
 
 
 @torch_op("aten::squeeze.dim", complex=True, trace_only=True)
@@ -7888,6 +7881,9 @@ def aten_squeeze_dim_complex(self: TTensor, dim: int) -> TTensor:
         # Account for the complex dimension in ONNX
         dim = dim - 1
 
+    if len(self.shape) == 1:
+        # The single dimension is the complex dimension
+        return self
     return aten_squeeze_dim(self, dim)
 
 
diff --git a/tests/function_libs/torch_lib/ops_test_data.py b/tests/function_libs/torch_lib/ops_test_data.py
index 1399264546..78d09c5f3c 100644
--- a/tests/function_libs/torch_lib/ops_test_data.py
+++ b/tests/function_libs/torch_lib/ops_test_data.py
@@ -1443,17 +1443,29 @@ def _where_input_wrangler(
     TorchLibOpInfo(
         "squeeze_dim",
         core_ops.aten_squeeze_dim,
-    ).skip(
+    )
+    .skip(
         matcher=lambda sample: not (len(sample.args) > 0 and isinstance(sample.args[0], int)),
         reason="this Aten overload only support one tensor as input and one int as args by design",
+    )
+    .skip(
+        matcher=lambda sample: len(sample.input.shape) != 0
+        and sample.input.shape[sample.args[0]] != 1,
+        reason="this Aten overload only support squeeze dim with size 1",
     ),
     TorchLibOpInfo(
         "squeeze_dim",
         core_ops.aten_squeeze_dim_complex,
         complex=True,
-    ).skip(
+    )
+    .skip(
         matcher=lambda sample: not (len(sample.args) > 0 and isinstance(sample.args[0], int)),
         reason="this Aten overload only support one tensor as input and one int as args by design",
+    )
+    .skip(
+        matcher=lambda sample: len(sample.input.shape) != 0
+        and sample.input.shape[sample.args[0]] != 1,
+        reason="this Aten overload only support squeeze dim with size 1",
     ),
     TorchLibOpInfo(
         "squeeze",